Computation Methods in Statistical and Quantum Mechanics

将研究开发和应用 统计力学中的计算方法和算法， 量子凝聚态物理学的相关领域。 发展 方法的主要特点是次优势的计算 转移矩阵本征值和激发态能量，其中 主要的应用将是（i）临界状态下的普遍振幅 phemonena和量子自旋链;（ii）弛豫时间 随机动力学谱;（iii）蒙特卡罗误差模型 分析;及（iv）Lennard-Jones玻色子的激发态性质 集群 另一个主题是关于 振幅的表面波动（几何和其他） 表征本体临界下的润湿层。 最后我们 我建议开发一个系统的可改进的近似方案 对于计算有限温度热力学， 量子链 %%% 将进行理论和计算研究，以提高 计算技术用于处理的相互作用， 大量的粒子。 一些不同的系统将 研究，以证明开发的技术。 成功 该项目的完成将提供技术， 适用于各种重要的计算密集型 问题

Research will be conducted on the development and application of computational methods and algorithms in statistical mechanics and related areas in quantum condensed matter physics. The development of methods predominantly features computation of subdominant transfer matrix eigenvalues and excited state energies, where the main applications will be (i) universal amplitudes in critical phemonena and quantum spin chains; (ii) the relaxation time spectrum of stochastic dynamics; (iii) models for Monte Carlo error analysis; and, (iv) excited state properties of Lennard-Jones boson clusters. Another topic is the universality with respect to surface fluctuations (geometric and other) of amplitudes characterizing wetting layers at bulk criticality. Lastly, we propose to develop a systematically improvable approximation scheme for the computation of the finite temperature thermodynamics of quantum chains. %%% Theoretical and computational research will be done to improve computational techniques used in dealing with the interactions of large numbers of particles. A number of different systems will be studied to demonstrate the developed techniques. The successful completion of this project will provide techniques which are applicible to a variety of important computationally intensive problems.